An extension of the associated rational functions on the unit circle

A special class of orthogonal rational functions (ORFs) is presented in this paper. Starting with a sequence of ORFs and the corresponding rational functions of the second kind, we define a new sequence as a linear combination of the previous ones, the coefficients of this linear combination being self-reciprocal rational functions. We show that, under very general conditions on the self-reciprocal coefficients, this new sequence satisfies orthogonality conditions as well as a recurrence relation. Further, we identify the Caratheodory function of the corresponding orthogonality measure in terms of such self-reciprocal coefficients. The new class under study includes the associated rational functions as a particular case. As a consequence of the previous general analysis, we obtain explicit representations for the associated rational functions of arbitrary order, as well as for the related Caratheodory function. Such representations are used to find new properties of the associated rational functions.Comment: 27 page

Determinants of soil organic matter chemistry in maritime temperate forest ecosystems

While the influence of climate, vegetation, management and abiotic site factors on total carbon budgets and turn-over is intensively assessed, the influences of these ecosystem properties on the chemical complexity of soil organic matter (SOM) remains poorly understood. This study addresses the chemical composition of NaOH-extracted SOM from maritime temperate forest sites in Flanders (Belgium) by pyrolysis-GC/MS. The studied forests were chosen based on dominant tree species (Pinus sylvestris, Fagus sylvatica, Quercus robur and Populus spp.), soil texture and soil-moisture conditions. Differences in extractable-SOM pyrolysis products were correlated to site variables including dominant tree species, management of the woody biomass, site history, soil properties, total carbon stocks and indicators for microbial activity. Despite of a typical high intercorrelation between these site variables, the influence of the dominant tree species is prominent. The extractable-SOM composition is strongly correlated to litter quality and available nutrients. In nutrient-poor forests with low litter quality, the decomposition of relatively recalcitrant compounds (i.e. short and mid-chain alkanes/alkenes and aromatic compounds) appears hampered, causing a relative accumulation of these compounds in the soil. However, if substrate quality is favorable, no accumulations of recalcitrant compounds were observed, not even under high soil-moisture conditions. Former heathland vegetation still had a profound influence on extractable-SOM chemistry of young pine forests after a minimum of 60 year

Promoting global watershed management towards rural communities: the May Zeg-zeg initiativeLength: pp.192-195

Watershed managementRural development

Veganism

Narrowly understood, veganism is the practice of excluding all animal products from one’s diet, with the exception of human milk. More broadly, veganism is not only a food ethics, but it encompasses all other areas of life. As defined by the Vegan Society when it became an established charity in the UK in 1979, veganism is best understood as “a philosophy and way of living which seeks to exclude – as far as is possible and practicable – all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of humans, animals and the environment”. There are two main moral justifications for veganism, both of which rely on a common assumption: that sentience, i.e., the capacity to feel pleasure and pain, is the necessary and sufficient trait to be morally considerable. In what follows, I present these two justifications and a third one which, although less popular, captures some core intuitions among vegans. I then present a challenge faced by veganism and two arguments that reject it as discriminatory, and briefly conclude

Lessons from contemporary trials of cardiovascular prevention and rehabilitation: A systematic review and meta-analysis

Background: Meta-analyses of cardiac rehabilitation trials up to 2010 showed a significant reduction in all-cause mortality but many of these trials were conducted before the modern management of acute coronary syndromes. Methods: We undertook a meta-analysis of contemporary randomised controlled trials published in the period 2010 to 2015, including patients with other forms of atherosclerotic cardiovascular disease, to investigate the impact of cardiovascular prevention and rehabilitation on hard outcomes including survival. Results: 18 trials randomising 7691 patients to cardiovascular prevention and rehabilitation or usual care were selected. All-cause mortality was not reduced (RR 1.00, 95% CI 0.88 to 1.14), but cardiovascular mortality was by 58% (95% CI 0.21, 0.88). Myocardial infarction was also reduced by 30% (95% CI 0.54, 0.91) and cerebrovascular events by 60% (95% CI 0.22, 0.74). Comprehensive programmes managing six or more risk factors reduced all-cause mortality in a subgroup analysis (RR 0.63, 95% CI 0.43, 0.93) but those managing less did not. In the three programmes that prescribed and monitored cardioprotective medications for blood pressure and lipids all-cause mortality was also reduced (RR 0.35, 95% CI 0.18, 0.70). Conclusions: Comprehensive prevention and rehabilitation programmes managing six or more risk factors, and those prescribing and monitoring medications within programmes to lower blood pressure and lipids, continue to reduce all-cause mortality. In addition, these comprehensive programmes not only reduced cardiovascular mortality and myocardial infarction but also, for the first time, cerebrovascular events, and all these outcomes across a broader spectrum of patients with atherosclerotic disease